arXiv subjects

Stefan Bachmann

Publications and source records attributed to Stefan Bachmann.

4 recordsLinked to original sources

arXiv2020

On the Strong Feller Property and Well-Posedness for SDEs with Functional, Locally Unbounded Drift

We study functional stochastic differential equations with a locally unbounded, functional drift focusing on well-posedness, stability and the strong Feller property. Following the non-functional case, we only consider integrability conditions and avoid continuity assumptions as far as possible. Our approach is mainly based on Zvonkin's transformation [18], an extended version of the probabilistic approach of Maslowski and Seidler [12] and the convergence concept for random variables in topological spaces in [2].

math.PR↗

arXiv2020

On the Strong Feller Property of Stochastic Delay Differential Equations with Singular Drift

In this paper, we prove the strong Feller property for stochastic delay (or functional) differential equations with singular drift. We extend an approach of Maslowski and Seidler to derive the strong Feller property of those equations. The argumentation is based on the well-posedness and the strong Feller property of the equations' drift-free version. To this aim, we investigate a certain convergence of random variables in topological spaces in order to deal with discontinuous drift coefficients.

math.PR↗

arXiv2019

On the Probabilistic Representation of the Free Effective Resistance of Infinite Graphs

We completely characterize when the free effective resistance of an infinite graph can be expressed in terms of simple hitting probabilities of the graphs random walk.

math.PR↗

arXiv2017

Well-Posedness and Stability for a Class of Stochastic Delay Differential Equations with Singular Drift

In this paper we prove well-posedness and stabibility of a class of stochastic delay differential equations with singular drift. Moreover, we show local well-posedness under localized assumptions.

math.PR↗